A dynamical system modeling the HIV infection, including a mutation occurrence process, is used, after simplifications, to show the impact of the viral diversity on the immune response and disease dynamics, by introducing an indicator of the immune system behavior, the immunological recognition efficacy (IRE) index. The existence, the expression and the stability of the endemically infected steady state of the IRE index-based model, as function of this index, are mathematically analyzed. The monotony of the steady state with respect to the IRE index is studied and an asymptotic analysis of the dynamical system performed. It is shown that the IRE index-based model provides a bound to the responses of the initial complex dynamical system. The biological interpretation of these mathematical results is the exhaustion of the immune system as a consequence of the continuous generation of viral mutants.